Proper cocycles and weak forms of amenability

Paul Jolissaint. "Proper cocycles and weak forms of amenability." Colloquium Mathematicae 138.1 (2015): 73-87. <http://eudml.org/doc/283498>.

@article{PaulJolissaint2015,
abstract = {Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard space (X,μ) such that $L^\{∞\}(X,μ)$ has an invariant mean and that there is a Borel cocycle α: G × X → H which is proper in the sense of Jolissaint (2000) and Knudby (2014). We show that if H has one of the three properties: Haagerup property (a-T-menability), weak amenability or weak Haagerup property, then so does G. In particular, we show that if Γ and Δ are measure equivalent discrete groups in the sense of Gromov, then such cocycles exist and Γ and Δ share the same weak amenability properties above.},
author = {Paul Jolissaint},
journal = {Colloquium Mathematicae},
keywords = {weak amenability; Haagerup property; cocycles; measure equivalent groups},
language = {eng},
number = {1},
pages = {73-87},
title = {Proper cocycles and weak forms of amenability},
url = {http://eudml.org/doc/283498},
volume = {138},
year = {2015},
}

TY - JOUR
AU - Paul Jolissaint
TI - Proper cocycles and weak forms of amenability
JO - Colloquium Mathematicae
PY - 2015
VL - 138
IS - 1
SP - 73
EP - 87
AB - Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard space (X,μ) such that $L^{∞}(X,μ)$ has an invariant mean and that there is a Borel cocycle α: G × X → H which is proper in the sense of Jolissaint (2000) and Knudby (2014). We show that if H has one of the three properties: Haagerup property (a-T-menability), weak amenability or weak Haagerup property, then so does G. In particular, we show that if Γ and Δ are measure equivalent discrete groups in the sense of Gromov, then such cocycles exist and Γ and Δ share the same weak amenability properties above.
LA - eng
KW - weak amenability; Haagerup property; cocycles; measure equivalent groups
UR - http://eudml.org/doc/283498
ER -